If we firstly consider only the terms in x.
subtract 2x from both sides of the equation
⇒5+2x
−2x=2x−2x
+6
Observe that the x terms are eliminated and we are left with
5+0=0+6 that is 5=6 which is invalid
There is no solution to this equation.
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2.
H - head
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T) = 0.8
urn
3 red and 5 blue
when heads is obtained
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12
when tails is obtained
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3
using bayes rule the answer can be found out,
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
= 0.12 / (0.12 + 0.3)
= 0.12 / 0.42
= 0.286
the final answer is 0.286
Answer:
x = -3
i explained it in the picture
Note: a² - b² = (a-b)(a+b)
9x² - 16y² = (3x)² - (4y)² = (3x - 4y)(3x + 4y)
Out of 12 rolls the tail appeared 8 times
So this experimental probability =8/12 = 2/3 (answer c)
